Corner case for ipopt when target_min = target_max

[SGeeversAtVortech]

In GitLab by @tpiovesan on Mar 1, 2019, 18:52

Say, we have a state V with initial state $V(t_0) = V_0$.
Moreover, we add a path goal on V with target_min = target_max = $V0$.

Then, the constraints added during goal programming will be:

• $V(t_0) - eps*\alpha_1 - V0 \geq 0$
• $V(t_0) - eps*\alpha_2 - V0 \leq 0$

where $\alpha_1, \alpha_2$ are constants, which together with

• $V(t_0) = V0$

may create convergence problems to ipopt since, if $\alpha_1 = \alpha_2$, we are not satisfying the LICQ condition. (Similar problem if we move the constraint to the bound.)

A possible solution is to use two different epsilons for the constraints instead of a single one.

I have not witness this case and this is a very particular situation. However, it's more likely to happen if/when we move constraints to bounds (because then then this will break LICQ even when $\alpha_1 \neq \alpha_2$). So we should keep this case in mind.